The Integrability Condition of Three-Dimensional Exactly Solvable Model-Baxter-Bazhanov Model in Statistical Mechanics

Hu Zhanning; Hou Boyu

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2024年10月30日

Chinese Physics C> 1995, Vol. 19> Issue(2) : 123-130

The Integrability Condition of Three-Dimensional Exactly Solvable Model-Baxter-Bazhanov Model in Statistical Mechanics

Hu Zhanning ^, ,
Hou Boyu

Institute of Modern Physics.Northwest University,Xi'an 710069

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Abstract：
From the chiral Potts model the"inversion"and"star-square"relations of the Baxter-Bazhanov model are obtained.This means that the tetrahedron equation which is a commutativity condition for the three-dimensional cubic lattice is a consequence of the star-triangle relation of the chiral Potts model.The additional constraints in tetrahedron equation hold naturally when the Boltzmann weights are parametrized in terms of the Zamolodchikov angle variables.It is point out that the star-triangle relation of the three-dimensional model can be gotten by using the method given in this paper,which includes the result of Baxter and Bazhanov's.

References

[1]

R.J.Baxter,Exactly solved models in statistical mechanics（Academic Press,London,1982）.[2]V.V.Bazhanov,R.J.Baxter,J.Stat.Phys.,69（1992）453.[3]A.B.Zamolodchikov.Commun.Math.Phys.,79（1981）489. [4]R.M.Kashaev,V.V.Mangazeev,Yu.G.Stroganov,Int.J.Mod.Phys.,A8（1993）1399.[5]R.J.Baxter,J.H.H.Perk,Phys.Lett.,A128（1988）138.V.B.Matveev,A.O.Smirnov,Some Comments on the Solvable Chiral Potts Model,pre-print.[6]V.V.Bazhanov,R.J.Baxter,J.Stat.Phys.,71（1993）839.[7]R.M.Kashaev,V.V.Mangazeev,Yu.G.Stroganov,Int.J.Mod.Phys.,A8（1993）587.

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Hu Zhanning and Hou Boyu. The Integrability Condition of Three-Dimensional Exactly Solvable Model-Baxter-Bazhanov Model in Statistical Mechanics[J]. Chinese Physics C, 1995, 19(2): 123-130.

Hu Zhanning and Hou Boyu. The Integrability Condition of Three-Dimensional Exactly Solvable Model-Baxter-Bazhanov Model in Statistical Mechanics[J]. Chinese Physics C, 1995, 19(2): 123-130. shu

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Received: 1900-01-01
Revised: 1900-01-01

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The Integrability Condition of Three-Dimensional Exactly Solvable Model-Baxter-Bazhanov Model in Statistical Mechanics

Hu Zhanning ^,
Hou Boyu

Corresponding author: Hu Zhanning,

Institute of Modern Physics.Northwest University,Xi'an 710069

Received Date: 1900-01-01
Accepted Date: 1900-01-01
Available Online: 1995-02-05

Abstract: From the chiral Potts model the"inversion"and"star-square"relations of the Baxter-Bazhanov model are obtained.This means that the tetrahedron equation which is a commutativity condition for the three-dimensional cubic lattice is a consequence of the star-triangle relation of the chiral Potts model.The additional constraints in tetrahedron equation hold naturally when the Boltzmann weights are parametrized in terms of the Zamolodchikov angle variables.It is point out that the star-triangle relation of the three-dimensional model can be gotten by using the method given in this paper,which includes the result of Baxter and Bazhanov's.